If he counted them, then he could have given a better calculation than “2/11”, since he had one additional prior that was unstated: the probability that he himself was (or was not) a male virtuist. In the same scenario, the best candidate would ask what the virtuist heresy was first, and then give an answer based on that additional information. (If the interrogator refused to answer, the answer might still be 2⁄11.)
Or it could already have been included in the calculation. If perhaps there had been 47 people in the room including 6 male virtuists and 5 male non-virtuists, and then Brennan arrives, a male non-virtuist, he makes all the numbers work out with 48 people and 33 virtuists of whom 6 are male (2/11).
But in fact we know it wasn’t, because there are an odd number of people in the room!
If he counted them, then he could have given a better calculation than “2/11”, since he had one additional prior that was unstated: the probability that he himself was (or was not) a male virtuist. In the same scenario, the best candidate would ask what the virtuist heresy was first, and then give an answer based on that additional information. (If the interrogator refused to answer, the answer might still be 2⁄11.)
Or, perhaps, the “if” rightly implied a hypothetical scenario, and the contents of the room as he perceived them were entirely irrelevant.
I had guessed something like that was the reason why the answer was supposed to be 1⁄6.
He might not know what a Virtuist is—it may be an arbitrary label for the purpose of this test, in which case the answer would not change.
Or it could already have been included in the calculation. If perhaps there had been 47 people in the room including 6 male virtuists and 5 male non-virtuists, and then Brennan arrives, a male non-virtuist, he makes all the numbers work out with 48 people and 33 virtuists of whom 6 are male (2/11).
But in fact we know it wasn’t, because there are an odd number of people in the room!